Adding to pennington:
Searches must be conducted only with the permission of the driver or when legally allowed (arrest, etc). If the officer's only justification for the search is the fact that the driver is a teenager, that would be grounds for a lawsuit. If anything is found, it would be grounds for dismissal of the evidence. However, if you find yourself in this situation express your objections politely but never fight or battle an officer (verbally or physically). Allow it and fight it later.
On the other hand, if there is another reason (driver has green leafy stuff on his shirt, joint in plain view, odour of marijauna, etc., previous history of drug use, etc) then there could be lawful justification.
It all depends on the situation.
Hope this helps,
Good luck

Legally, he can't search (pretty much like geek860 said). However, very often a cop will ask if he can search. If you say yes, then he can search and everything he finds can be used against you.
It is amazing how often people will say yes to a search, even when they know they have things they don't want found.
see the video at
http://www.youtube.com/watch?v=yqMjMPlXzdA
for a good guide to how to protect your rights when you encounter the police.

He can do anything he wants to you, and you will be a criminal if you resist, or even complain.
He can even drag you off and beat or rape you, and you are not permitted to resist. If you are a girl, you'd better be ugly and stinky, or you are toast.
None of it is legal, of course, but he can do it.

No, he cannot search. Know Your Rights!
The SCOTUS recently (April 2009) scaled back police search powers in Arizona vs. Gant.
The justices said that an arresting officer could search a vehicle only if weapons were potentially in reach of the suspect or if there was reason to believe that the car contained evidence related to the arrest. For example, if the driver was arrested in a drug crime, the car could be searched for drugs.
Justice John Paul Stevens, speaking for the court, said that merely arresting a driver does not "provide a police entitlement" to search the vehicle without a warrant.
He said the court's past rulings had given police too much leeway, allowing them to search cars even when there was no threat to officers' safety. For example, if a motorist was handcuffed and put in a patrol car, there was no danger that he could reach a weapon in his car.
The lineup behind Stevens was unusual. Justices Antonin Scalia, David H. Souter, Clarence Thomas and Ruth Bader Ginsburg formed the majority.
The case arose when Rodney Gant was arrested in Tucson for driving with a suspended license. His car was parked in his driveway, and officers handcuffed Gant and put him in a patrol car. Then they searched the car and found a gun and cocaine in a jacket in the back seat.
Gant was convicted on drug charges, but the Arizona Supreme Court threw out evidence on the grounds that the search of his car without a warrant was unreasonable.
The U.S. Supreme Court affirmed that decision Tuesday in Arizona vs. Gant.
The dissenters, led by Justice Samuel A. Alito Jr., said the court should have stuck with the old rule that permitted vehicle searches whenever a driver or an occupant was arrested.

Legally they need probable cause. Probable cause means police must have some facts or evidence to believe you're involved in criminal activity. In other words, an officer's hunch without evidence of illegal activity is not enough to legally search your car. Before searching, he must observe something real.

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